Speaking ASA/Fed, are there provisions to correct errors in any given contest, such as in basketball?? Like before the next out, before the next half/full inning, before the second live ball following a dead ball, etc... TIA

Almost always before the next pitch. Managers can protest mistaken rulings (not judgement calls), managers can appeal missed bases, batting out of order. Umpires can correct situations where their own error put one side at jeopardy.

Don't forget about the next play. it does not have to be a pitch. It could be a pickoff play too.

And by pitch, it does not have to be a legal one. Illegal ones count towards this too.

I have never quite grasped the "uncorrectable" errors RE: Infield Fly Rule. I have been told that:
1) If we call it, and it was in fact was not an I.F. situation..too bad. Players should had known we blew it while it was happening. ie we call Infield fly and no one catches the ball. The batter stops running, and leaves the field. Coach says "Hey-she's not out". Too bad we can't fix it.
2) We forget to call I.F., & then the ball is not caught. Coach says "Hey blue-she's out right ?", we say OH yeah I forgot. We can't fix that one either ?
.
So why is it that the Ump clearly misapplied the rule in both cases, and yet they are not protestable, or correctable.

IFR
 

Regarding Sitch #2 I believe Rule 7-4-1h indicates the batter is out even if the IFR is not called.

Regarding Sitch #1 i will let others answer that one.

Infield Fly is a judgment call. I think if you called an Infield Fly and say you didn't have runners on 1,2, or 1,2,3. that is a missed rule and you could fix it.

Sitch 1 - runners and fielders (and yes, umpires) should know the sitch. Not correctable, as no one SHOULD HAVE been in jeopardy had they been aware of the true situation.

Sitch 2 is definitely correctable.

Read this in NFHS Guide,

[QUOTE]A veteran umpire once erroneously called an IF in a game with runners
on second and third. Slick fielding all-star SS looked straight at the umpire
and said, "IF?" Quickly realizing the error, the umpire pointed at her and said,
"You'd better catch it!" Laughing at the reply, she easily moved under the
ball to make the catch.
Obviously, an improperly declared infield fly is <b>not</b> an infield fly.

There are two parts to the IFR; one part is rule, and is correctable if misapplied, the other part is judgment, and cannot be corrected.

Part one, rule application, is calling an infield fly when the rule does not apply, OR not calling it when it does apply. This is correctable if misapplied, just like any other misapplied rule. If that placed a runner or defender in jeopardy, then that is correctable, but it takes a big stretch, IMO. Runners and fielders are expected to know if the IFR is applicable.

Part two, judgment, is the "can be caught with ordinary effort" decision. That part cannot be reconsidered or corrected, no matter how badly the judgment may appear after the play is over.